Disordered Monomer-Dimer Model on Cylinder Graphs

Partha S. Dey, Kesav Krishnan

Research output: Contribution to journalArticlepeer-review


We consider the disordered monomer-dimer model on cylinder graphs Gn , i.e., graphs given by the Cartesian product of the line graph on n vertices, and a deterministic finite graph. The edges carry i.i.d. random weights, and the vertices also have i.i.d. random weights, not necessarily from the same distribution. Given the random weights, we define a Gibbs measure on the space of monomer-dimer configurations on Gn . We show that the associated free energy converges to a limit and, with suitable scaling and centering, satisfies a Gaussian central limit theorem. We also show that the number of monomers in a typical configuration satisfies a law of large numbers and a Gaussian central limit theorem with appropriate centering and scaling. Finally, for an appropriate height function associated with a matching, we show convergence to a limiting function and prove the Brownian motion limit around the limiting height function in the sense of finite-dimensional distributional convergence.

Original languageEnglish (US)
Article number146
JournalJournal of Statistical Physics
Issue number8
StatePublished - Aug 2023


  • Central limit theorems
  • Disordered systems
  • Monomer-dimer models
  • Random dimer activities

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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